High-resolution radio imaging of two luminous quasars beyond redshift 4.5

Context. Radio-loud active galactic nuclei in the early Universe are rare. The quasars J0906+6930 at redshift z=5.47 and J2102+6015 at z=4.57 stand out from the known sample with their compact emission on milliarcsecond (mas) angular scale with high (0.1-Jy level) flux densities measured at GHz radio frequencies. This makes them ideal targets for very long baseline interferometry (VLBI) observations. Aims. By means of VLBI imaging we can reveal the inner radio structure of quasars and model their brightness distribution to better understand the geometry of the jet and the physics of the sources. Methods. We present sensitive high-resolution VLBI images of J0906+6930 and J2102+6015 at two observing frequencies, 2.3 and 8.6 GHz. The data were taken in an astrometric observing programme involving a global five-element radio telescope array. We combined the data from five different epochs from 2017 February to August. Results. For one of the highest redshift blazars known, J0906+6930, we present the first-ever VLBI image obtained at a frequency below 8 GHz. Based on our images at 2.3 and 8.6 GHz, we confirm that this source has a sharply bent helical inner jet structure within ~3 mas from the core. The quasar J2102+6015 shows an elongated radio structure in the east-west direction within the innermost ~2 mas that can be described with a symmetric three-component brightness distribution model at 8.6 GHz. Because of their non-pointlike mas-scale structure, these sources are not ideal as astrometric reference objects. Our results demonstrate that VLBI observing programmes conducted primarily with astrometric or geodetic goals can be utilized for astrophysical purposes as well.Comment: 8 pages, 3 figures, accepted for publication in Astronomy & Astrophysic

Classical Tensors and Quantum Entanglement II: Mixed States

Invariant operator-valued tensor fields on Lie groups are considered. These define classical tensor fields on Lie groups by evaluating them on a quantum state. This particular construction, applied on the local unitary group U(n)xU(n), may establish a method for the identification of entanglement monotone candidates by deriving invariant functions from tensors being by construction invariant under local unitary transformations. In particular, for n=2, we recover the purity and a concurrence related function (Wootters 1998) as a sum of inner products of symmetric and anti-symmetric parts of the considered tensor fields. Moreover, we identify a distinguished entanglement monotone candidate by using a non-linear realization of the Lie algebra of SU(2)xSU(2). The functional dependence between the latter quantity and the concurrence is illustrated for a subclass of mixed states parametrized by two variables.Comment: 23 pages, 4 figure

A Note on Normal Forms of Quantum States and Separability

We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the entanglement witness is further constructed in terms of local orthogonal observables for both bipartite and multipartite systems.Comment: 8 page

Avaliação das alterações na cobertura vegetal de área no Estado do Mato Grosso do Sul entre 1990 e 2010 por meio de imagens Landsat TM.

Imagens Landsat/TM dos anos de 1990 e 2010 de área no Estado de Mato Grosso do Sul foram transformadas em imagens de reflectância e classificadas quanto à presença, ao porte e à densidade de cobertura vegetal do solo, com base nos valores calculados de NDVI e de reflectância na banda do infravermelho próximo (ρivp). Pela fusão digital das imagens classificadas de ambos os anos foi possível tipificar e quantificar as alterações ocorridas no período. Áreas da classe delimitada pelos valores de NDVI entre 0,55 e 0,75, associadas em sua maioria às pastagens, cobriam 60,2% da área de estudo em 1990 e 64,0% em 2010. As áreas da classe associada à vegetação densa com grande presença de espécies arbóreas (cerrado e matas de galeria) foram reduzidas de 31,1% para 24,5% no mesmo período, redução provocada, sobretudo, pelo aumento das áreas com pastagens. As lavouras com vegetação herbácea verde cobrindo completamente o solo na data de aquisição das imagens e algumas áreas de silvicultura foram associadas a valores de NDVI acima de 0,75 e ρivp ≥ 0,40 e totalizaram áreas equivalentes a 4,3% da área de estudo em 1990 e 2,2 % em 2010. As áreas com vegetação esparsa ou ausente compreendiam menos de 10% da área de estudo em ambos os anos, e normalmente estavam associadas a pastagens com sinais de degradação, locais destinados a lavouras, solo exposto, feições urbanas e corpos d?água

Cortes compensados para la deformación principal alpina en el borde sur oriental del Sistema Central español (Zona de Tamajón, Guadalajara)

Las estructuras alpinas principales del borde sur oriental del Sistema Central Español (zona de Tamajón) resultan ser dos cabalgamientos de dirección N70oE, con dirección de transporte hacia el SE, con retrocabalgamientos y fallas de transferencia asociadas. La dirección de transporte de los cabalgamientos es coherente con la dirección de acortamiento horizontal de la "etapa Guadarrama" (N1500E), a la cual están asociados genéticamente. El efecto de los cabalgamientos en la cobertera mesozoica es el desarrollo de diferentes tipos de pliegues asimétricos. El acortamiento, deducido de la restauración de cortes geológicos, es de 17-19

Double collinear splitting amplitudes at next-to-leading order

We compute the next-to-leading order (NLO) QCD corrections to the 1 -> 2 splitting amplitudes in different dimensional regularization (DREG) schemes. Besides recovering previously known results, we explore new DREG schemes and analyze their consistency by comparing the divergent structure with the expected behavior predicted by Catani's formula. Through the introduction of scalar-gluons, we show the relation among splittings matrices computed using different schemes. Also, we extended this analysis to cover the double collinear limit of scattering amplitudes in the context of QCD+QED

Further results on entanglement detection and quantification from the correlation matrix criterion

The correlation matrix (CM) criterion is a recently derived powerful sufficient condition for the presence of entanglement in bipartite quantum states of arbitrary dimensions. It has been shown that it can be stronger than the positive partial transpose (PPT) criterion, as well as the computable cross norm or realignment (CCNR) criterion in different situations. However, it remained as an open question whether there existed sets of states for which the CM criterion could be stronger than both criteria simultaneously. Here, we give an affirmative answer to this question by providing examples of entangled states that scape detection by both the PPT and CCNR criteria whose entanglement is revealed by the CM condition. We also show that the CM can be used to measure the entanglement of pure states and obtain lower bounds for the entanglement measure known as tangle for general (mixed) states.Comment: 13 pages, no figures; added references, minor changes; section 4.3 added, to appear in J. Phys.

Classical Tensors and Quantum Entanglement I: Pure States

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form. The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map. This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry. Here we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states. Geometrical tensors are shown to encode some properties of these states. These results are not unrelated with criteria already available in the literature. We explicitly deal with some of these relations.Comment: 16 pages, 1 figure, to appear in Int. J. Geom. Meth. Mod. Phy